Rodrigues’ rotation formula

Rodrigues’ rotation formula gives a convenient way to write the general rotation matrix in $R^3$.

If $[v_1,v_2,v_3]$ is a unit vector on the rotation axis, and $\theta$ is the rotation angle about that axis, then the rotation matrix is given by

$$I+\sin (\theta )A+(1-\cos (\theta ))A^2$$

where $I$ is the identity matrix and

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